Install the Alexa toolbar or Firefox’s SearchStatus extension and set your blog as your homepage. This is the most basic step.
Put up an Alexa rank widget on your website. I did this a few days ago and receive a fair amount of clicks every day. According to some, each click counts as a visit even if the toolbar is not used by the visitor.
Encourage others to use the Alexa toolbar. This includes friends, fellow webmasters as well as site visitors/blog readers. Be sure to link to Alexa’s full explanation of their toolbar and tracking system so your readers know what installing the toolbar or extension entails.
Work in an Office or own a company? Get the Alexa toolbar or SS Firefox extension installed on all computers and set your website as the homepage for all browsers. Perhaps it will be useful to note that this may work only when dynamic or different IPs are used.
Get friends to review and rate your Alexa website profile. Not entirely sure of its impact on rankings but it might help in some way.
Write or Blog about Alexa. Webmaster and bloggers love to hear about ways to increase their Alexa rank. They’ll link to you and send you targeted traffic (i.e. visitors with the toolbar already installed). This gradually has effects on your Alexa ranking.
Flaunt your URL in webmaster forums. Webmasters usually have the toolbar installed. You’ll get webmasters to visit your website and offer useful feedback. It’s also a good way to give back to the community if you have useful articles to share with others.
Write content that is related to webmasters. This can fall in the category of domaining and SEO, two fields in which most webmasters will have the Alexa toolbar installed. Promote your content on social networking websites and webmaster forums.
Use Alexa redirects on your website URL. Try this: http://redirect.alexa.com/redirect?www.doshdosh.com . Replace doshdosh.com with the URL for your website. Leave this redirected URL in blog comments as well as forum signatures. This redirect will count a unique IP address once a day so clicking it multiple times won’t help.
Post in Asian social networking websites or forums. Some webmasters have suggested that East Asian web users are big Alexa toolbar fans, judging by the presence of several Asia-based websites in the Alexa Top 500. I suggest trying this only if you have the time or capacity to do so.
Create a webmaster tools section on your website. This is a magnet for webmasters who will often revisit your website to gain access to the tools. Aaron Wall’s webpage on SEOTools is a very good example.
Some more ways at http://bit.ly/Increase-Alexa-Rank